Respuesta :
The rule of the volume of the hemisphere is
[tex]V=\frac{2}{3}\pi r^3[/tex]r is the radius of it
Since the diameter of the hemisphere is double the radius, then we can find the radius then multiply it by 2 to find it
Since the volume of the hemisphere is 841 cm^3, then
Substitute V by 841
[tex]\begin{gathered} 841=\frac{2}{3}\pi(r^3) \\ 841=\frac{2}{3}\pi r^3 \end{gathered}[/tex]Divide both sides by 2/3pi
[tex]\begin{gathered} \frac{841}{\frac{2}{3}\pi}=\frac{\frac{2}{3}\pi r^3}{\frac{2}{3}\pi} \\ \\ \frac{2523}{2\pi}=r^3 \end{gathered}[/tex]Take cube root to both sides
[tex]\begin{gathered} \sqrt[3]{\frac{2523}{2\pi}}=\sqrt[3]{r^3} \\ 7.377555082=r \end{gathered}[/tex]Multiply it by 2 to find the diameter, then round it to the nearest tenth
[tex]\begin{gathered} d=7.377555082\times2 \\ d=14.75511016 \\ d=14.8\text{ cm} \end{gathered}[/tex]The diameter of the hemisphere is 14.8 cm
